Boolean elements in the Bruhat order on twisted involutions

Delong Meng

doi:10.2140/involve.2012.5.339

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Home > Journals > Involve > Volume 5 > Issue 3 > Article

2012 Boolean elements in the Bruhat order on twisted involutions

Delong Meng

Involve 5(3): 339-348 (2012). DOI: 10.2140/involve.2012.5.339

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Abstract

We prove that a permutation in the Bruhat order on twisted involutions is Boolean if and only if it avoids the following patterns: 4321, 3421, 4312, 4231, 32541, 52143, 351624, 456123, 426153, 321654, 561234, 345612, 3416275, 3561274, 1532746, 4517236, 34127856, 35172846, and 36712845. This result answers a question proposed by Hultman and Vorwerk. Our technique provides an application of the pictorial representation of the Bruhat order given by Incitti.